Q81 / 150 · MHT CET 2017 · Mathematics

A random variable $X ∽ B (n, p) .$ If values of mean and variance of $X$ are $18$ and $12$ respectively then total number of possible values of $X$ are

A
$54$
Correct answer
B
$55$
C
$12$
D
$18$

Solution

Mean = np = 18
Variance = npq = 12

\Rightarrow

\frac{n p q}{n p} = \frac{12}{18}

\Rightarrow

q = \frac{2}{3}

\Rightarrow

p = 1 - q = 1 - \frac{2}{3}

\Rightarrow

p = \frac{1}{3}

Now

n p = 18

\Rightarrow

n (\frac{1}{3}) = 18

\Rightarrow

n = 54

\Rightarrow

∴

Values of

X

are
0, 1, 2, ........... 54

∴ 55

Values.

Hence, the correct answer is option: 'B'.

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